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Pointwise Partial Information Decomposition Using the Specificity and Ambiguity Lattices.

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  • 1Complex Systems Research Group and Centre for Complex Systems, Faculty of Engineering & IT, The University of Sydney, NSW 2006, Australia.

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Summary
This summary is machine-generated.

This study introduces a new method for information decomposition, analyzing how predictor variables uniquely, redundantly, or synergistically inform a target variable using specificity and ambiguity measures.

Keywords:
complementary informationinformation decompositionmutual informationpointwise informationredundancyredundant informationsynergyunique information

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Area of Science:

  • Information theory
  • Machine learning
  • Statistical modeling

Background:

  • Understanding how predictor variables relate to a target variable is crucial in many fields.
  • Existing information decomposition methods, like the redundancy lattice, face challenges with their measures of redundant information.
  • A need exists for a robust framework to analyze multivariate information decomposition.

Purpose of the Study:

  • To develop a novel approach for multivariate information decomposition.
  • To address limitations of existing methods by applying axiomatic derivation to discrete variables.
  • To propose new measures for redundant specificity and ambiguity to evaluate information atoms.

Main Methods:

  • Applying the axiomatic derivation of the redundancy lattice to discrete variable realizations.
  • Decomposing pointwise mutual information into specificity and ambiguity components.
  • Defining and measuring redundant specificity and ambiguity.
  • Recombining information atoms to achieve multivariate information decomposition.

Main Results:

  • Developed separate redundancy lattices for specificity and ambiguity.
  • Introduced measures for redundant specificity and ambiguity.
  • Demonstrated the framework's application to canonical examples.
  • Showcased a chain rule property for target variables in the pointwise decomposition.

Conclusions:

  • The proposed framework offers a new perspective on information decomposition.
  • Specificity and ambiguity measures provide a more satisfactory analysis of redundant information.
  • The method yields insights into complex information interactions, such as in the two-bit-copy example.